Linear and inverse contracts
Two contracts reference the same asset, you hold the same nominal size in each, the price moves the same distance — and the two positions do not change in value by the same amount.
The reason is not a difference in the underlying. It is that a derivative has to be denominated in something, and there are two common choices. That single decision determines the arithmetic of the payoff, which currency your margin sits in, and whether a fixed contract count means a fixed exposure.
The one difference that generates all the others
Every contract has a contract size — a stated amount that one contract represents — and that amount is expressed in one of the two currencies in the pair.
A linear contract is sized in the base asset. One contract represents some quantity of the thing being referenced, and margin and settlement are in the quote currency.
An inverse contract is sized in the quote currency. One contract represents a fixed amount of quote value, and margin and settlement are in the base asset.
Everything else follows mechanically from that. Which currency your gains arrive in, whether the number of contracts describes your exposure, and whether the payoff is a straight line are all consequences, not separate facts to memorise.
Linear contracts
Sized in base, settled in quote. The profit or loss on a position is the quantity of base multiplied by the price change, in quote units.
That expression is linear in price, which is where the name comes from. A move of a given size produces the same quote-denominated result whether it happens from a high price or a low one, and the position’s sensitivity to price does not change as price changes.
Two practical properties. Exposure is what it says: a position of a stated quantity of base is exposure to that quantity, at every price. And collateral is independent of the underlying — margin posted in the quote currency does not itself change in value as the referenced asset moves, so the margin ratio moves for one reason rather than two.
Inverse contracts
Sized in quote, settled in base. A position of some quote-denominated notional corresponds to a quantity of base equal to that notional divided by the current price.
Which means the quantity of the underlying your position represents changes as the price changes, even though your contract count does not. The contract count fixes the value, not the quantity, and the quantity is the thing that determines how the position responds to the next move.
Profit and loss is denominated in the base asset, and its expression involves the reciprocal of price rather than price itself. That is not a formatting difference. A reciprocal is a curve, so the position’s base-denominated response to a move is not constant.
Why the inverse payoff curves
Take a long inverse position and follow it in the currency it settles in.
As the price rises, each further increment adds less base-denominated profit than the one before, because the base quantity your fixed quote notional represents is shrinking. The gain converges — an arbitrarily large rise cannot produce more base than the position’s initial base equivalent.
As the price falls, each further decrement costs more base than the one before, because the base quantity your notional represents is growing. The loss diverges: there is no bound on the base figure as the price approaches zero.
A short inverse position has the mirror shape — bounded base-denominated loss on the way up, unbounded base-denominated gain on the way down.
Neither of these is a defect and neither is a recommendation. What it is, mechanically, is an asymmetry that has to be measured in the settlement currency to be visible at all. Convert the same position back into quote units and it looks ordinary again, which is exactly why the asymmetry is easy to miss: the interface may be showing you one currency while your collateral sits in the other.
The mechanism
THE MECHANISM — denomination and payoff
· Linear contract, sized in base
→ P&L in quote, linear in price.
Contract count is exposure.
· Inverse contract, sized in quote
→ P&L in base, reciprocal in price.
Contract count is value, not
quantity.
· Inverse position, price moves far your way
→ base gain converges. It cannot
exceed the initial base
equivalent.
· Inverse position, price moves far against
you
→ base loss diverges. NO BOUND as
the price approaches zero.
· Inverse margin in the base asset
→ collateral and exposure are the
same asset. The margin ratio moves
for two reasons at once.
· A fixed contract count on an inverse
→ NO GUARANTEE of fixed exposure.
The underlying quantity changes
with price.
· Contract sizes, multipliers, which
products are inverse, and quanto variants
→ VENUE-SPECIFIC. Some venues list
both forms on the same asset.Worked example
Illustrative figures, synthetic throughout, and deliberately round so the arithmetic is checkable.
Suppose a reference price of 40,000 quote per base. A linear long of 1.0 base: at 50,000 the position has gained 1.0 × 10,000 = 10,000 quote. At 30,000 it has lost 10,000 quote. Symmetric, and the sensitivity is 1.0 base per unit of price throughout.
Now an inverse long of 40,000 quote notional at the same reference price. That is a base equivalent of 40,000 ÷ 40,000 = 1.0 base at entry — the same starting exposure.
At 50,000: the base equivalent of the notional is now 40,000 ÷ 50,000 = 0.8. The gain is the difference, 1.0 − 0.8 = 0.2 base, which converted at 50,000 is 10,000 quote — the same quote result as the linear position.
At 80,000: base equivalent 0.5, gain 0.5 base. At 400,000: base equivalent 0.1, gain 0.9 base. The base gain is walking towards 1.0 and will never reach it.
At 30,000: base equivalent 40,000 ÷ 30,000 ≈ 1.333, loss ≈ 0.333 base. At 20,000: base equivalent 2.0, loss 1.0 base — the entire base amount the position started as, at half the price. At 10,000: loss 3.0 base.
The quote-denominated results match the linear contract at every point. The base-denominated results do not resemble each other at all, and the base is what the margin is posted in.
Contract counts, multipliers and quanto
Three further layers of indirection, all of which change what a quantity field means.
The contract multiplier. One contract may represent many units of whatever it is denominated in, so the smallest increment of position is one contract, which is coarser than a spot step size. A position that is not a whole number of contracts is not expressible.
Which currency the quantity box wants. Some interfaces accept base, some quote, some contracts, and some let you switch. The same number typed into the same-looking field can be three different orders.
Quanto contracts. A third form, where the payoff is calculated on one pair and settled in an unrelated currency at a fixed conversion. This introduces exposure to a rate that has nothing to do with the pair you chose, and it is a distinct thing again from either linear or inverse.
The failure mode
The characteristic error is arithmetic done in the wrong currency. An inverse position looks well-behaved when displayed in quote terms, because in quote terms it is; the divergence lives in the base figures, and the base figures are the ones the margin engine is looking at.
That produces a specific, quiet consequence. On an inverse position margined in the base asset, a move against you does two things at once: it increases the base-denominated loss faster than linearly, and it changes the value of the collateral itself. Both effects push the margin ratio the same way, and the mark price the venue liquidates against is unaffected by which of the two you were tracking.
None of this makes either form better or worse, and this site takes no position on which anyone should hold. What is mechanically true is that the denomination is not a labelling convention — it is part of the instrument, and a position sized correctly in one form is not the same position sized identically in the other.